Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  double H;
  cin >> n >> H;
  double area = 0.5 * H;
  double fArea = area / n;
  double b = 1, tanT = 2 * H;
  vector<double> heights;
  cerr << fArea << endl;
  for (int i = 0; i < n - 1; i++) {
    double selected = (b - sqrt(b * b - ((4 * fArea) / tanT))) / (2 / tanT);
    heights.push_back(selected);
    b -= 2 * selected / tanT;
    cerr << i << " " << selected << " " << b << endl;
  }
  vector<double> ans;
  double prevH = 0;
  for (int i = 0; i < n - 1; i++) {
    ans.push_back(H - prevH - heights[i]);
    prevH += heights[i];
  }
  sort(ans.begin(), ans.end());
  for (int i = 0; i < n - 1; i++) {
    printf("%.7f ", ans[i]);
  }
  cout << endl;
}